On the Uniqueness in the Inverse Conductivity Problem

Abstract

Let $\Omega$ be a smooth domain in R² containing a polygon D. The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered. We show that D is uniquely determined from boundary measurements corresponding two appropriately chosen Neumann datas.